Vietnam's foreign minister has asked his Indonesian counterpart to investigate and clarify reports that the Indonesian navy shot and wounded two Vietnamese fishermen in the East Sea, the Vietnamese reference for the South China Sea.

Pham Binh Minh, who is also Vietnam's deputy prime minister, told Indonesian foreign minister Retno Marsudi by telephone on Friday that the reported incident was "very serious ... and not appropriate with the strategic partnership relationship between Vietnam and Indonesia," the Vietnamese foreign ministry said in a statement.

"Vietnam is deeply concerned about this incident and requests that Indonesia quickly investigate and clarify the incident and inform Vietnam of the results and to stop repeating similar acts," Minh was quoted as saying.

A foreign ship allegedly fired at a Vietnamese fishing boat from the central province of Binh Dinh last Saturday, about 132 nautical miles (245 km) southeast of Vietnam's Con Dao Island.

Two of the fishermen on the Vietnamese boat were seriously injured by the shooting and were flown to a major hospital in Ho Chi Minh City on Tuesday for treatment.

Indonesia has denied claims that its navy was responsible for the shooting. Vietnam has, however, identified the ship as the Indonesian navy ship, according to its foreign ministry.

Although Indonesia says it is not a party to the dispute, it recently renamed the northern reaches of its exclusive economic zone, asserting its own maritime claim.

The coordinates given by the Vietnamese search and rescue committee indicated that the shooting happened close to the area Indonesia now calls the North Natuna Sea, Reuters reported.

Indonesia has sunk hundreds of mostly foreign boats caught illegally fishing in its waters since President Joko Widodo launched a crackdown on the poaching of fish in 2014, the newswire said.

Indonesia and Vietnam said in May they would launch a joint investigation after reports that Vietnamese coast guards had tried to forcibly free five fishing boats and their crew detained in waters near Indonesia's Natuna Islands, according to Reuters.